MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN K Problems
14
14
Part of
PEN K Problems
Problems
(1)
K 14
Source:
5/25/2007
Find all functions
f
:
Z
→
Z
f:\mathbb{Z} \to \mathbb{Z}
f
:
Z
→
Z
such that for all
m
∈
Z
m\in\mathbb{Z}
m
∈
Z
: [*]
f
(
m
+
8
)
≤
f
(
m
)
+
8
f(m+8) \le f(m)+8
f
(
m
+
8
)
≤
f
(
m
)
+
8
, [*]
f
(
m
+
11
)
≥
f
(
m
)
+
11
f(m+11) \ge f(m)+11
f
(
m
+
11
)
≥
f
(
m
)
+
11
.
function
inequalities
Functional Equations